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## Chapter 2 Linear Equations in One Variable Exercise 2.5

Solve the following linear equations.
Question 1: x/2 - 1/5 = x/3 + 1/4

= x/2 - x/3 = 1/4 + 1/5
= 3x/6 - 2x/6 = 5/20 + 4/20
= 1x/6 = 9/20
= 1x = 9/20 × 6
= x = 54/20
= x = 27/10

Question 2: n/2 - 3n/4 + 5n/6 = 21

= 6n/12 - 9n/12 + 10n/12 = 21
= 7n/12 = 21
= 7n = 21 × 12
= 7n = 252
= n = 252/7
= n = 36

Question 3: x + 7 - 8x/3 = 17/6 - 5x/2

= x/1 + 7/1 - 8x/3 = 17/6 - 5x/2
= x/1 - 8x/3 + 5x/2 = 17/6 - 7/1
= 6x/6 - 16x/6 + 15x/6 = 17/6 - 42/6
= 5x/6 = -25/6
= 5x = -25
= x = -25/5
= x = -5

Question 4: (x - 5)/3 = (x - 3)/5

= x/3 - 5/3 = x/5 - 3/5
= x/3 - x/5 = -3/5 + 5/3
= 5x/15 - 3x/15 = -9/15 + 25/15
= 2x/15 = 16/15
= 2x = 16
= x = 16/2
= x = 8

Question 5: (3t - 2)/4 - (2t + 3)/3 = 2/3 - t

= 3t - 2/4 × 12 - 2t + 3/3 × 12 = 2/3 × 12 - t × 12
= 3t - 2 × 3 - 2t + 3 × 4 = 2 × 4 - 12t
= 9t - 6 - 8t - 12 = 8 - 12t
= t - 18 = 8 - 12t
= t + 12t = 8 + 18
= 13t = 26
= t = 26/13
= t = 2

Question 6: m - (m - 1)/2 = 1 - (m - 2)/3

= m × 6 - m - 1/2 × 6 = 1 × 6 - m - 2/3 × 6
= 6m - m - 1 × 3 = 6 - m  - 2 × 2
= 6m - 3m + 3 = 6 - 2m + 4
= 3m + 3 = 10 - 2m
= 3m + 2m = 10 - 3
= m = 7/5

Simplify and solve the following linear equations.
Question 7: 3(t - 3) = 5(2t + 1)

= 3t - 9 = 10t + 5
= 3t - 10t = 5 + 9
= -7t = 14
= t = 14/-7
= t = -2

Question 8: 15(y - 4) -2(y - 9) + 5(y + 6) = 0

= 15y - 60 - 2y + 18 + 5y + 30 = 0
= 8y - 12 = 0
= 8y = 0 + 12
= 8y = 12
= y = 12/8
= y = 3/2

Question 9: 3(5z - 7) - 2(9z - 11) = 4(8z - 13) - 17

= 15z - 21 - 18z + 22 = 32z - 52 - 17
= -3z + 1 = 32z - 69
= -3z - 32z = -69 - 1
= -35z = -70
= 35z = 70
= z = 70/35
= z = 2

Question 10: 0.25(4f - 3) = 0.05(10f - 9)